I have a circle with an arc beginning at point (x,y). The radius is r, the arc angle(w/ respect to center) is θ. How do I calculate the end point of the arc (a,b) ?I know that the arc-length=radius*(arc angle)I can't seem to find an easy way to solve this, I think the way to go is with parametric equations but I'm not sure.

Question

I have a circle with an arc beginning at point (x,y). The radius is r, the arc angle(w/ respect to center) is   θ. How do I calculate the end point of the arc (a,b) ?I know that the arc-length=radius*(arc angle)I can&#039;t seem to find an easy way to solve this, I think the way to go is with parametric equations but I&#039;m not sure.

Sophia Mcdowell · Accepted Answer

One way is to calculate the angle to the first point  α  =  arctan  ⁡      (                  p        1.        y        −        c        p        .        y                    p        1.        x        −        c        p        .        x              )  Then you add your angle and calculate the new point:  p  2.  x  =  c  p  .  x  +  r  ∗  c  o  s  (  α  +  θ  )  p  2.  y  =  c  p  .  y  +  r  ∗  s  i  n  (  α  +  θ  )